Compound interest, explained with your own numbers
Compound interest is what happens when growth earns its own growth. This calculator projects how an initial amount and regular contributions could grow over time, lets you compare savings-goal scenarios, and shows exactly which assumptions drive the result - so you can see the mechanics, not just a single headline number.
How to use the calculator
Start with the three essentials: an initial investment (zero is fine), a regular contribution and how often you make it, and a duration. Add an illustrative annual return - this is an assumption you choose, never a guarantee or a prediction of real market performance.
The calculator has three modes. “Future value” projects your balance from the inputs you give it. “Required savings” flips the question: tell it a target balance, and it solves for the regular contribution needed to reach it. “Time to goal” solves for how long reaching a target would take at your current contribution rate. Switch modes any time - your other inputs carry over.
Open “More settings” for contribution timing, an annual contribution increase, the choice between a nominal and an effective rate, fees, inflation, a simplified tax assumption, and one-off deposits. None of these are required - the calculator works perfectly well with just the three essentials above.
What compound interest actually is
Simple interest pays you a fixed amount each period, calculated only on your original principal. Compound interest pays you on your principal plus every bit of growth you've already earned - so your return itself starts earning a return. The gap between the two grows slowly at first and then visibly, the longer the money stays invested.
This only works through reinvestment. If growth is paid out and spent rather than left to compound, there's nothing for the next period to grow on top of - you're back to something closer to simple interest in practice, however the account is labeled. That's the entire mechanical story behind every “start early” argument you'll read elsewhere: an extra five years isn't just five more years of the same growth, it's five more years for the growth itself to start generating growth.
None of this requires a bank account specifically. The same mathematics applies to a reinvested dividend, a fund that doesn't distribute its gains, or - carefully, see the FAQ below - a long-run average on a diversified portfolio. What changes between those cases isn't the compounding math, it's how reliably and smoothly the underlying return actually behaves, which this calculator deliberately doesn't try to simulate.
The formulas behind the projection, and why timing matters
For a single lump sum with no further contributions, the future value after n periods at a per-period rate i is:
P is your starting amount, and i and n have to use matching periods - an annual rate with years, or (as this calculator actually does internally) a monthly rate with months. At zero growth, this collapses to simply P, your money unchanged, which is a useful sanity check whenever you're testing a formula.
Add a constant regular contribution C, paid at the end of every period, and the future value becomes:
This closed-form formula assumes the contribution stays genuinely constant at that same interval throughout. The calculator itself doesn't rely on this shortcut at all - it always simulates every month individually, which is what lets it also handle an annual contribution increase, one-off deposits, fees, and tax precisely rather than approximately. At zero growth, the formula above simplifies to P + Cn: your principal plus every contribution, with no growth at all, exactly what you'd expect.
Timing changes the result. A contribution paid at the beginning of a period gets one more period of growth than the same contribution paid at the end - multiply only the contribution term, C × ((1+i)ⁿ − 1) / i, by (1+i) and you get the beginning-of-period (“annuity-due”) version; the lump-sum term P(1+i)ⁿ is unaffected, since the initial investment's own timing never changes. Over many contributions, that one extra period per payment adds up to a real, calculable amount - never dramatic for any single contribution, but consistent and genuine across the whole schedule, which is exactly why this calculator lets you choose either timing rather than assuming one.
Three worked examples
Every figure below comes directly from this calculator's own engine, not a separately hand-calculated estimate - enter the same assumptions into the calculator above to reproduce any of them exactly and explore further.
A lump sum, left alone
€10,000 invested once, no further contributions, at a 5% effective annual return, left for 10 years: the projected balance is 16,288.95 € - 6,288.95 € of that is growth, on top of your original €10,000. Nothing else changes this example: no fees, no tax, no inflation adjustment, so it isolates the pure effect of compounding on its own.
A regular saving plan
No starting capital, €200 saved at the end of every month, at the same 5% effective annual return, over 20 years: the projected balance is 81,160.90 €. You would have paid in 48,000.00 € of your own money over that period - the remaining 33,160.90 € is growth, nearly as much as you contributed yourself, a useful illustration of why duration tends to matter more than most people expect.
Solving for a savings goal
Start with €5,000, aim for a €100,000 balance in 20 years, same 5% effective return: the required-savings mode of this calculator solves for a monthly contribution of 213.74 € - saving exactly that much, with nothing else changed, projects to a balance of 100,003.14 €, at or just above the target, since this calculator always rounds a solved contribution up to the next cent rather than down.
As a variation worth trying yourself: apply a 3% annual increase to Example 2's €200 monthly contribution (the “More settings” panel), and the same 20-year projection rises to 103,971.62 € on 64,488.90 € paid in - a real, calculable effect, not a rounding artifact, from letting your own savings rate grow roughly alongside your income over time.
What actually affects how much you end up with
Four things move the final number, and they don't all move it the same way. Time is usually the strongest lever, since it's the one factor that compounds on itself - the gap between 10 years and 20 years of growth is often far more than double, even with identical contributions and the same assumed rate, because the extra years let early growth keep generating its own growth.
Contribution size matters too, but linearly rather than compounding on itself - doubling your monthly contribution roughly doubles the portion of your balance that came from contributions, without the same snowball effect time has. The assumed return matters enormously over a long horizon and barely at all over a short one; a one-percentage-point difference in assumed return can change a 30-year projection by tens of thousands of euros, and a 2-year projection by almost nothing.
And reinvestment is the quiet precondition behind all of it - every one of these factors assumes growth stays in the account rather than being withdrawn along the way. None of this implies markets reliably deliver any particular return; it describes how a given assumed return compounds, not whether that return will actually occur. See the FAQ below on why an average annual return isn't the same thing as a smooth compound annual growth rate.
Inflation and fees: what they actually touch
Inflation never changes your nominal balance or your contribution schedule in this calculator - it only changes how that same nominal number is translated into today's purchasing power, shown as a separate figure. €100,000 in 20 years is still €100,000 in 20 years' money; whether that buys as much as €100,000 does today depends entirely on how prices move between now and then, which is exactly what the purchasing-power figure is trying to show you.
Fees work differently: they're a real, ongoing deduction from the balance itself, applied every month as a small percentage reduction, which means they compound against you the same way growth compounds for you. A fee that looks small annually can meaningfully erode a long projection, which is why this calculator applies it as a genuine monthly deduction rather than simply subtracting it from your assumed return - and why there's a toggle for “the return I entered already accounts for this fee”, so a fee never gets deducted twice by accident.
German tax context, and what this tool's tax switch does and doesn't do
Investment income in Germany is generally subject to Abgeltungsteuer (a flat 25% withholding tax on capital gains, interest, and dividends), plus the solidarity surcharge and, where applicable, church tax - together often summarized as a combined rate in the high 20s percent. Every saver also has a Sparer-Pauschbetrag, an annual tax-free allowance for investment income (€1,000 for a single person, €2,000 for a jointly-assessed married couple, as of this writing - confirm the current figure with your Finanzamt or a tax advisor, since allowances can change by law) - income below that allowance in a given year isn't taxed at source, provided you've filed a Freistellungsauftrag with your bank or broker; without one, the tax is withheld anyway and the allowance can still be claimed back via your annual tax return instead.
This calculator's own tax option is a deliberately simplified stand-in for that system, not a replica of it. Switch it on, and it applies your entered combined percentage to each modeled year's gross growth above the remaining allowance you specify, once a year, at a clean 12-month boundary.
What it does not do matters just as much: it doesn't model the Vorabpauschale (an annual notional-gain charge that applies to many funds even before you sell), fund partial exemptions (Teilfreistellung, which reduce the taxable share of equity-fund gains), loss offsetting across years, foreign withholding tax on non-German investments, or the basic reality that a real capital gain is usually taxed only once you actually sell, not smoothly every year the way this model assumes for simplicity.
If you want an actual German capital-gains calculation rather than this illustrative stand-in, this site's own capital-gains calculator is built for exactly that. Treat this tool's tax switch as a way to see the general shape of tax's effect on long-term growth, not as a number to put on a tax return.
Reading scenarios and projections for what they are
Every chart and number this calculator produces is a smooth, deterministic projection: the same assumed return applied every single month, with no randomness and no bad years. Real markets don't behave that way - returns vary year to year, sometimes sharply negative, and the smooth line this calculator draws is a simplification chosen for clarity, not a claim about how an actual investment's balance would move month to month.
Use the scenario comparison to see how sensitive your own result is to the assumption you're least sure about - usually the return, sometimes the contribution amount - rather than to predict which scenario is “right”. A lower-return scenario that still meets your goal is worth more peace of mind than a single optimistic number that only works if everything goes well.